If-A-and-B-are-two-indpendent-events-the-probability-that-both-A-and-B-occur-is-1-8-and-the-probability-that-neither-of-them-occurs-is-3-8-The-probability-of-the-occurrence-of-A-is-

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Question Number 81925 by zainal tanjung last updated on 16/Feb/20

$$\mathrm{If}A\mathrm{and}B\mathrm{are}\mathrm{two}\mathrm{indpendent}\mathrm{events},$$$$\mathrm{the}\mathrm{probability}\mathrm{that}\mathrm{both}A\mathrm{and}B\mathrm{occur}$$$$\mathrm{is}\frac{1}{8}\mathrm{and}\mathrm{the}\mathrm{probability}\mathrm{that}\mathrm{neither}\mathrm{of}$$$$\mathrm{them}\mathrm{occurs}\mathrm{is}\frac{3}{8}.\mathrm{The}\mathrm{probability}\mathrm{of}\mathrm{the}$$$$\mathrm{occurrence}\mathrm{of}A\mathrm{is}$$

Answered by MJS last updated on 16/Feb/20

$$\mathrm{both}:ab=\frac{1}{8}$$$$\mathrm{neither}:(1-a)(1-b)=\frac{3}{8}$$$$\Rightarrow a=\frac{1}{2}\wedge b=\frac{1}{4}\vee a=\frac{1}{4}\wedge b=\frac{1}{2}$$

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